Art is a skilled worker in a precision optical instrument factory. He is paid $1 per hour plus an additional $5 per hour for each microscope he assembles in that hour. If Art assembles a microscope every 20 minutes over the course of an 8 hour work day, what is Art’s resulting hourly wage, and how much does he make in a four week month with 5 work day months? Both parts of an answer must be correct. (a) $23/hour, $2,100/month (b) $16/hour, $2,400/month (c) $17/hour, 384 microscopes

(d) $20/hour, $1,920/month (e) $16/hour, $2,560/month (f) none of the above

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  (e)  $16/hour, $2560/month

Step-by-step explanation:

At one assembly per 20 minutes, Art assembles 3 microscopes per hour. That means each hour he gets paid $1 + 3×$5 = $16.

There are 8×5 = 40 hours in a work week, and 4×40 = 160 hours in a month. Art's pay for the month will be ...

  ($16/h)(160 h) = $2560

Art's pay is $16 per hour, and $2560 per month.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places